A bipartite graph is biplanar if the vertices can beplaced on two parallel lines in the plane such that there areno edge crossings when edges are drawn as straight-line segments.We study two variants of biplanarization problems:- Two-Layer Planarization TLP: can $k$ edges be deleted froma given graph $G$ so that the remaining graph is biplanar?- One-Layer Planarizatoin OLP: fix the order of the vertices on one layer.

Improving on earlier works of Dujmovi\'c et al., we solve the TLP problem in $O^*(5.19^k)$ time and theOLP problem in $O^*(2.53^k)$ time.